Question

A square tin sheet of 12 inches is converted into a box with open top in the following steps. The sheet is placed horizontally. Then, equal sized squares, each of side x inches, are cut from the four corners of the sheet. Finally, the four resulting sides are bent vertically upward in the shape of a box. If x is an integer, then what value of x maximizes the volume of the box?​

Answer 1

Answer:

128

Step-by-step explanation:

Volume of box = (12 - 2x) * (12 -2x) *  x

= 144x - 48$x^{2}$ + 4$x^{3}$

differentiate

=> 144 - 96x + 12$x^{2}$

solve for x

=> 144 -96x + 12$x^{2}$ = 0

=> $x^{2}$ - 8x + 12 = 0

=> x = 6, 2

put x in volume

x = 6 , v = 0

x = 2, v = 128 ans

Answer 2

Answer:

Step-by-step explanation:

128

Step-by-step explanation:

Volume of box = (12 - 2x) * (12 -2x) *  x

= 144x - 48 + 4

differentiate

=> 144 - 96x + 12

solve for x

=> 144 -96x + 12 = 0

=>  - 8x + 12 = 0

=> x = 6, 2

put x in volume

x = 6 , v = 0

x = 2, v = 128 is the answer